WASHINGTON — With the potential for an unprecedented federal default two weeks away, House Republicans on Wednesday plan to pass legislation not to avert disaster, but rather to manage it, channeling daily tax collections to the nation’s creditors and Social Security recipients if the government’s borrowing limit is not lifted.

The Obama administration and nonpartisan authorities say the plan is unworkable, but efficacy may be beside the point: Republican leaders appear to be buying time to find enough members of their own party to join Democrats in supporting an increase or suspension of the statutory debt limit by the Nov. 3 deadline so the nation can borrow to pay its bills — all of them — without a market-shaking crisis.

The challenge is daunting. The risk of the nation’s first default has increased along with the numbers of Tea Party Republicans who have entered Congress, many of them pledged to oppose any debt-limit increase. Standoffs over the issue in 2013 and 2011 caused measurable economic damage, including setbacks for Americans’ retirement accounts. If that story line has the ring of “boy cries wolf,” one financial analyst wrote in his newsletter to market investors this week, “At the end of the book, the wolf eats the boy.”

The legislative math has only grown more difficult. When Congress last voted in February 2014 to suspend the debt limit, 28 House Republicans joined nearly all Democrats in support; 199 Republicans were opposed. Now there are fewer Democrats in the House and if all 188 of them voted for an increase, Republican leaders would need 30 votes from their side for a 218-vote majority — two more than last year.

Yet nine of last year’s 28 Republican supporters have left Congress and at least three of their Republican successors — Representatives Dave Brat of Virginia, Steve Knight of California and Mark Walker, Republican of North Carolina — are almost certain to be opposed.

Also, 14 Democrats who voted to increase the debt limit are gone, replaced by Republicans, some of whom are likely to vote no.

“You have got to be able to say that something is big enough that you would shut down the government,” Mr. Knight told a California radio station on Friday. Mr. Knight, who replaced Howard McKeon, a Republican supporter of the last debt-ceiling increase, added, “We have got to stop digging at some point and make people understand that we have got to have a balanced budget that works on knocking down the deficit, or our children are going to have a much, much different country.”

Representative Kevin McCarthy of California, the majority leader, told reporters on Tuesday that he did not think a debt-ceiling increase could pass the House without significant spending cuts attached, a deal President Obama has repeatedly said he will not negotiate.

Chris Krueger of Guggenheim Securities, the Washington analyst who this week warned clients of the hazards ahead, predicted that the borrowing limit would be lifted.

“But we are basing that on nothing more than blind faith,” he said, adding, “To the best of our knowledge, the Treasury has never been in such a difficult position going into a debt ceiling showdown with Congress.”

The Treasury Department has recently seen lower-than-expected revenue collections, and it faces big payments in November for Social Security, military pay, federal salaries and interest to creditors. For seven months, when the government bumped up against the current $18.1 trillion debt limit, the Treasury has been taking so-called extraordinary measures — shifts among federal accounts that avoid the need for more cash. But those steps will be exhausted by Nov. 3, the Treasury secretary, Jacob J. Lew, told congressional leaders in a letter last week.

Leaders of the Republican-controlled Congress had long expected a December deadline. Now, facing the need for expedited action, they are beset by chaos. Hard-line conservatives pressed Speaker John A. Boehner to announce his resignation, leaving the party openly at war over a successor.

Those same conservatives, the roughly 40 members of the House Freedom Caucus, are emboldened to force the kind of debt-limit confrontation with Mr. Obama that they say Mr. Boehner shied away from.

“It’s a three-ring circus over there,” said Senator Chuck Schumer of New York, the Senate’s No. 3 Democrat, “which you might laugh at, except the consequences are so serious.”

A separate coalition of conservatives that includes most House Republicans, the Republican Study Committee, on Tuesday outlined conditions it would demand that Mr. Obama meet. These include $3.8 trillion in savings, mainly from entitlements like Medicare and Medicaid, and a balanced-budget constitutional amendment, which could not win congressional approval without the leverage of a debt crisis.

The proposal could come to a House vote by Friday.

“If we are going to increase the borrowing authority of the country, then we need to do something that actually addresses the big problem, the $19 trillion debt,” said Representative Jim Jordan, Republican of Ohio, who leads the Freedom Caucus. “We need to go out as a group and say, ‘Here we are, Mr. President, we’ll allow the borrowing authority to go up, if you do this.’ ”

Representative Justin Amash, Republican of Michigan, similarly said Congress first must act to reduce spending for Medicare, Medicaid and Social Security — the fast-growing benefit programs — and should not be deterred by warnings of tumult in the market and broader economy that some analysts say would inevitably follow default.

The market “will make its determinations,” Mr. Amash said. “But it’s more important for members of Congress to do the right thing in the long run that will be better for the stock market in the long run and convey the message that there’s no chance of default.”

On Tuesday, Senator Mitch McConnell of Kentucky, the majority leader, said the Senate would await House action. Senate Republicans, too, would like to attach some conditions, he said, but he declined to specify what those might include.

Yet with time running out, what the House will vote on Wednesday and send to the Senate falls far short of the needed debt-limit increase.

The “Default Prevention Act,” as Republicans call it, is a variation on their past proposals to give priority to certain obligations that can be covered by incoming tax receipts if the debt limit is breeched — in this case, creditors and the nation’s most politically popular program, Social Security. But the administration, like President George W. Bush’s before it, said that is unrealistic, since the 80 million payments each month are disbursed automatically and tax receipts fluctuate greatly.

“It would be untenable for the United States to pick and choose which payments to default on,” said a posting on the Treasury Department website. “It is simply default by another name” and “would undermine confidence in the creditworthiness of the United States.”

The White House issued a stern veto threat on Tuesday evening.

Privately, some Republicans concede the vote is a way for members to seem to oppose default. Douglas Holtz-Eakin, an economics adviser to Republicans and the former director of the nonpartisan Congressional Budget Office, called it “political cover but not a solution of any type.”

“There’s no way that you can pretend that taking out the Pentagon budget and a huge chunk of the domestic budget is not going to be damaging,” he said. “It will. And I don’t think international investors will be mollified by the fact they got their two bucks while the U.S. burned down.”

A version of this article appears in print on , on Page A16 of the New York edition with the headline: Lawmakers Wrangle Over Plans to Avert, Manage or Embrace Default. Order Reprints | Today’s Paper | Subscribe